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Ullah SA, Yang X, Jones B, Zhao S, Geng W, Wei GW. Bridging Eulerian and Lagrangian Poisson-Boltzmann solvers by ESES. J Comput Chem 2024; 45:306-320. [PMID: 37830273 PMCID: PMC10993026 DOI: 10.1002/jcc.27239] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Revised: 08/08/2023] [Accepted: 09/24/2023] [Indexed: 10/14/2023]
Abstract
The Poisson-Boltzmann (PB) model is a widely used electrostatic model for biomolecular solvation analysis. Formulated as an elliptic interface problem, the PB model can be numerically solved on either Eulerian meshes using finite difference/finite element methods or Lagrangian meshes using boundary element methods. Molecular surface generators, which produce the discretized dielectric interfaces between solutes and solvents, are critical factors in determining the accuracy and efficiency of the PB solvers. In this work, we investigate the utility of the Eulerian Solvent Excluded Surface (ESES) software for rendering conjugated Eulerian and Lagrangian surface representations, which enables us to numerically validate and compare the quality of Eulerian PB solvers, such as the MIBPB solver, and the Lagrangian PB solvers, such as the TABI-PB solver. Furthermore, with the ESES software and its associated PB solvers, we are able to numerically validate an interesting and useful but often neglected source-target symmetric property associated with the linearized PB model.
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Affiliation(s)
| | - Xin Yang
- Department of Mathematics, Southern Methodist University, Dallas, Texas, USA
| | - Ben Jones
- Department of Mathematics, Michigan State University, East Lansing, Michigan, USA
| | - Shan Zhao
- Department of Mathematics, University of Alabama, Tuscaloosa, Alabama, USA
| | - Weihua Geng
- Department of Mathematics, Southern Methodist University, Dallas, Texas, USA
| | - Guo-Wei Wei
- Department of Mathematics, Michigan State University, East Lansing, Michigan, USA
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Moreau A, Yaya F, Lu H, Surendranath A, Charrier A, Dehapiot B, Helfer E, Viallat A, Peng Z. Physical mechanisms of red blood cell splenic filtration. Proc Natl Acad Sci U S A 2023; 120:e2300095120. [PMID: 37874856 PMCID: PMC10622898 DOI: 10.1073/pnas.2300095120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2023] [Accepted: 09/02/2023] [Indexed: 10/26/2023] Open
Abstract
The splenic interendothelial slits fulfill the essential function of continuously filtering red blood cells (RBCs) from the bloodstream to eliminate abnormal and aged cells. To date, the process by which 8 [Formula: see text]m RBCs pass through 0.3 [Formula: see text]m-wide slits remains enigmatic. Does the slit caliber increase during RBC passage as sometimes suggested? Here, we elucidated the mechanisms that govern the RBC retention or passage dynamics in slits by combining multiscale modeling, live imaging, and microfluidic experiments on an original device with submicron-wide physiologically calibrated slits. We observed that healthy RBCs pass through 0.28 [Formula: see text]m-wide rigid slits at 37 °C. To achieve this feat, they must meet two requirements. Geometrically, their surface area-to-volume ratio must be compatible with a shape in two tether-connected equal spheres. Mechanically, the cells with a low surface area-to-volume ratio (28% of RBCs in a 0.4 [Formula: see text]m-wide slit) must locally unfold their spectrin cytoskeleton inside the slit. In contrast, activation of the mechanosensitive PIEZO1 channel is not required. The RBC transit time through the slits follows a [Formula: see text]1 and [Formula: see text]3 power law with in-slit pressure drop and slip width, respectively. This law is similar to that of a Newtonian fluid in a two-dimensional Poiseuille flow, showing that the dynamics of RBCs is controlled by their cytoplasmic viscosity. Altogether, our results show that filtration through submicron-wide slits is possible without further slit opening. Furthermore, our approach addresses the critical need for in vitro evaluation of splenic clearance of diseased or engineered RBCs for transfusion and drug delivery.
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Affiliation(s)
- Alexis Moreau
- Aix Marseille Université, CNRS, Centre Interdisciplinaire de Nanoscience de Marseille, Turing Centre for Living Systems, Marseille13009, France
| | - François Yaya
- Aix Marseille Université, CNRS, Centre Interdisciplinaire de Nanoscience de Marseille, Turing Centre for Living Systems, Marseille13009, France
| | - Huijie Lu
- Richard and Loan Hill Department of Biomedical Engineering, University of Illinois, Chicago, IL60612
| | - Anagha Surendranath
- Aix Marseille Université, CNRS, Centre Interdisciplinaire de Nanoscience de Marseille, Turing Centre for Living Systems, Marseille13009, France
| | - Anne Charrier
- Aix Marseille Université, CNRS, Centre Interdisciplinaire de Nanoscience de Marseille, Turing Centre for Living Systems, Marseille13009, France
| | - Benoit Dehapiot
- Aix Marseille Université, CNRS, Institut de Biologie du Développement de Marseille, Turing Centre for Living Systems, Marseille13009, France
| | - Emmanuèle Helfer
- Aix Marseille Université, CNRS, Centre Interdisciplinaire de Nanoscience de Marseille, Turing Centre for Living Systems, Marseille13009, France
| | - Annie Viallat
- Aix Marseille Université, CNRS, Centre Interdisciplinaire de Nanoscience de Marseille, Turing Centre for Living Systems, Marseille13009, France
| | - Zhangli Peng
- Richard and Loan Hill Department of Biomedical Engineering, University of Illinois, Chicago, IL60612
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Abstract
The present article is focused on the shapes of dendritic tips occurring in undercooled binary systems in the absence of convection. A circular/globular shape appears in limiting cases of small and large Péclet numbers. A parabolic/paraboloidal shape describes the tip regions of dendrites whereas a fractional power law defines a shape behind their tips in the case of low/moderate Péclet number. The parabolic/paraboloidal and fractional power law shapes are sewed together in the present work to describe the dendritic shape in a broader region adjacent to the dendritic tip. Such a generalized law is in good agreement with the parabolic/paraboloidal and fractional power laws of dendritic shapes. A special case of the angled dendrite is considered and analysed in addition. The obtained results are compared with previous experimental data and the results of numerical simulations on dendritic growth. This article is part of the theme issue 'Patterns in soft and biological matters'.
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Affiliation(s)
- Dmitri V. Alexandrov
- Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg 620000, Russian Federation
| | - Peter K. Galenko
- Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg 620000, Russian Federation
- Physikalisch-Astronomische Fakultät, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany
- e-mail:
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Trichtchenko O, Părău EI, Vanden-Broeck JM, Milewski P. Solitary flexural-gravity waves in three dimensions. Philos Trans A Math Phys Eng Sci 2018; 376:20170345. [PMID: 30126916 PMCID: PMC6107609 DOI: 10.1098/rsta.2017.0345] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 06/19/2018] [Indexed: 06/08/2023]
Abstract
The focus of this work is on three-dimensional nonlinear flexural-gravity waves, propagating at the interface between a fluid and an ice sheet. The ice sheet is modelled using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis, presented in (Plotnikov & Toland. 2011 Phil. Trans. R. Soc. A369, 2942-2956 (doi:10.1098/rsta.2011.0104)). The fluid is assumed inviscid and incompressible, and the flow irrotational. A numerical method based on boundary integral equation techniques is used to compute solitary waves and forced waves to Euler's equations.This article is part of the theme issue 'Modelling of sea-ice phenomena'.
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Affiliation(s)
- Olga Trichtchenko
- Department of Physics and Astronomy, University of Western Ontario, London, Ontario, Canada
| | - Emilian I Părău
- School of Mathematics, University of East Anglia, Norwich, UK
| | | | - Paul Milewski
- Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, UK
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Galenko PK, Alexandrov DV, Titova EA. The boundary integral theory for slow and rapid curved solid/liquid interfaces propagating into binary systems. Philos Trans A Math Phys Eng Sci 2018; 376:rsta.2017.0218. [PMID: 29311215 PMCID: PMC5784107 DOI: 10.1098/rsta.2017.0218] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/18/2017] [Indexed: 05/11/2023]
Abstract
The boundary integral method for propagating solid/liquid interfaces is detailed with allowance for the thermo-solutal Stefan-type models. Two types of mass transfer mechanisms corresponding to the local equilibrium (parabolic-type equation) and local non-equilibrium (hyperbolic-type equation) solidification conditions are considered. A unified integro-differential equation for the curved interface is derived. This equation contains the steady-state conditions of solidification as a special case. The boundary integral analysis demonstrates how to derive the quasi-stationary Ivantsov and Horvay-Cahn solutions that, respectively, define the paraboloidal and elliptical crystal shapes. In the limit of highest Péclet numbers, these quasi-stationary solutions describe the shape of the area around the dendritic tip in the form of a smooth sphere in the isotropic case and a deformed sphere along the directions of anisotropy strength in the anisotropic case. A thermo-solutal selection criterion of the quasi-stationary growth mode of dendrites which includes arbitrary Péclet numbers is obtained. To demonstrate the selection of patterns, computational modelling of the quasi-stationary growth of crystals in a binary mixture is carried out. The modelling makes it possible to obtain selected structures in the form of dendritic, fractal or planar crystals.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.
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Affiliation(s)
- Peter K Galenko
- Physikalisch-Astronomische Fakultät, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany
| | - Dmitri V Alexandrov
- Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg 620000, Russian Federation
| | - Ekaterina A Titova
- Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg 620000, Russian Federation
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Abstract
Recently, the authors presented two numerical studies for capturing the flow structure beneath water waves (Nachbin and Ribeiro-Junior 2014 Disc. Cont. Dyn. Syst. A34, 3135-3153 (doi:10.3934/dcds.2014.34.3135); Ribeiro-Junior et al. 2017 J. Fluid Mech.812, 792-814 (doi:10.1017/jfm.2016.820)). Closed orbits for irrotational waves with an opposing current and stagnation points for rotational waves were some of the issues addressed. This paper summarizes the numerical strategies adopted for capturing the flow beneath irrotational and rotational water waves. It also presents new preliminary results for particle trajectories, due to irrotational waves, in the presence of a bottom topography.This article is part of the theme issue 'Nonlinear water waves'.
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Affiliation(s)
- A Nachbin
- IMPA/National Institute of Pure and Applied Mathematics, Estr. D. Castorina 110, Jardim Botânico, Rio de Janeiro, RJ 22460-320, Brazil
| | - R Ribeiro-Junior
- Departamento de Matemática, UFPR/Universidade Federal do Paraná, Centro Politécnico, Jardim das Américas, Caixa Postal 19081, Curitiba, PR 81531-980, Brazil
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Abstract
Studies on the deformation behaviours of cellular entities, such as coated microbubbles and liposomes subject to a cavitation flow, become increasingly important for the advancement of ultrasonic imaging and drug delivery. Numerical simulations for bubble dynamics of ultrasound contrast agents based on the boundary integral method are presented in this work. The effects of the encapsulating shell are estimated by adapting Hoff's model used for thin-shell contrast agents. The viscosity effects are estimated by including the normal viscous stress in the boundary condition. In parallel, mechanical models of cell membranes and liposomes as well as state-of-the-art techniques for quantitative measurement of viscoelasticity for a single cell or coated microbubbles are reviewed. The future developments regarding modelling and measurement of the material properties of the cellular entities for cutting-edge biomedical applications are also discussed.
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Affiliation(s)
- Qianxi Wang
- School of Mathematics , University of Birmingham , Birmingham B15 2TY , UK
| | - Kawa Manmi
- School of Mathematics , University of Birmingham , Birmingham B15 2TY , UK ; Department of Mathematics, College of Science , Salahaddin University-Erbil , Kurdistan Region , Iraq
| | - Kuo-Kang Liu
- School of Engineering , University of Warwick , Coventry CV4 7AL , UK
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Abstract
A bubble initiated near a rigid boundary may be almost in contact with the boundary because of its expansion and migration to the boundary, where a thin layer of water forms between the bubble and the boundary thereafter. This phenomenon is modelled using the weakly compressible theory coupled with the boundary integral method. The wall effects are modelled using the imaging method. The numerical instabilities caused by the near contact of the bubble surface with the boundary are handled by removing a thin layer of water between them and joining the bubble surface with its image to the boundary. Our computations correlate well with experiments for both the first and second cycles of oscillation. The time history of the energy of a bubble system follows a step function, reducing rapidly and significantly because of emission of shock waves at inception of a bubble and at the end of collapse but remaining approximately constant for the rest of the time. The bubble starts being in near contact with the boundary during the first cycle of oscillation when the dimensionless stand-off distance γ = s/R m < 1, where s is the distance of the initial bubble centre from the boundary and R m is the maximum bubble radius. This leads to (i) the direct impact of a high-speed liquid jet on the boundary once it penetrates through the bubble, (ii) the direct contact of the bubble at high temperature and high pressure with the boundary, and (iii) the direct impingement of shock waves on the boundary once emitted. These phenomena have clear potential to damage the boundary, which are believed to be part of the mechanisms of cavitation damage.
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Affiliation(s)
- Qianxi Wang
- School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK
| | - Wenke Liu
- School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK
| | - A. M. Zhang
- College of Shipbuilding Engineering, Harbin Engineering University, 145, Nantong Street, Harbin, People's Republic of China
| | - Yi Sui
- School of Engineering and Materials Science, Queen Mary University of London, London E1 4NS, UK
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Dupont C, Delahaye F, Barthès-Biesel D, Salsac AV. Time required for an oblate capsule in flow to reach equilibrium. Comput Methods Biomech Biomed Engin 2014; 17 Suppl 1:36-7. [PMID: 25074152 DOI: 10.1080/10255842.2014.931091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- C Dupont
- a Laboratoire BMBI, UMR CNRS 7338 , Université de Technologie de Compiègne , Compiègne , France
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